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IEEE International Symposium on Circuits and Systems (ISCAS)

作者： Hu, SQ Liu, DR Zhang, HG Univ Illinois Dept Elect & Comp Engn Chicago IL 60607 USA

ISBN: (纸本)0780388348

This paper presents gradient-based methods for simultaneous blind separation of arbitrarily mixed source signals. We consider the regular case where the mixing matrix has full column rank as well as ill-conditioned cases. Two cost functions based on fourth-order cumulants are introduced to simultaneously separate all separable single sources and all inseparable mixtures. By minimizing the cost functions, two gradient-based methods are developed. Our algorithms derived from gradient-based methods are guaranteed to converge. Finally, simulation results show the effectiveness of our methods.

关键词： blind source separation cumulants gradient-based methods ill-conditioned cases independence

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Backpropagation through signal temporal logic specifications: Infusing logical structure into gradient-based methods

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INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH 2023年第6期42卷 356-370页

作者： Leung, Karen Arechiga, Nikos Pavone, Marco Stanford Univ 496 Lomita MallRm 261 Stanford CA 94305 USA Toyota Res Inst Los Altos CA USA

This paper presents a technique, named STLCG, to compute the quantitative semantics of Signal Temporal Logic (STL) formulas using computation graphs. STLCG provides a platform which enables the incorporation of logical specifications into robotics problems that benefit from gradient-based solutions. Specifically, STL is a powerful and expressive formal language that can specify spatial and temporal properties of signals generated by both continuous and hybrid systems. The quantitative semantics of STL provide a robustness metric, that is, how much a signal satisfies or violates an STL specification. In this work, we devise a systematic methodology for translating STL robustness formulas into computation graphs. With this representation, and by leveraging off-the-shelf automatic differentiation tools, we are able to efficiently backpropagate through STL robustness formulas and hence enable a natural and easy-to-use integration of STL specifications with many gradient-based approaches used in robotics. Through a number of examples stemming from various robotics applications, we demonstrate that STLCG is versatile, computationally efficient, and capable of incorporating human-domain knowledge into the problem formulation.

关键词： Signal Temporal Logic backpropagation computation graphs gradient-based methods

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Discrete optimization via gradient-based adaptive stochastic search methods

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IISE TRANSACTIONS 2018年第9期50卷 789-805页

作者： Chen, Xi Zhou, Enlu Hu, Jiaqiao Univ Illinois Dept Ind & Enterprise Syst Engn Champaign IL USA Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA SUNY Stony Brook Dept Appl Math & Stat Stony Brook NY 11794 USA

gradient-based Adaptive Stochastic Search (GASS) is a new stochastic search optimization algorithm that has recently been proposed. It iteratively searches promising candidate solutions through a population of samples generated from a parameterized probabilistic model on the solution space, and updates the parameter of the probabilistic model based on a direct gradient method. Under the framework of GASS, we propose two discrete optimization algorithms: discrete gradient-based Adaptive Stochastic Search (discrete-GASS) and annealing gradient-based Adaptive Stochastic Search (annealing-GASS). In discrete-GASS, we transform the discrete optimization problem into a continuous optimization problem on the parameter space of a family of independent discrete distributions, and apply a gradient-based method to find the optimal parameter, such that the corresponding distribution has the best capability to generate optimal solution(s) to the original discrete problem. In annealing-GASS, we use a Boltzmann distribution as the parameterized probabilistic model, and propose a gradient-based temperature schedule that changes adaptively with respect to the current performance of the algorithm. We show convergence of both discrete-GASS and annealing-GASS under appropriate conditions. Numerical results on several benchmark optimization problems and the traveling salesman problem indicate that both algorithms perform competitively against a number of other algorithms, including model reference adaptive search, the cross-entropy method, and multi-start simulated annealing with different temperature schedules.

关键词： Stochastic search gradient-based methods discrete optimization

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A survey on multi-objective, model-based, oil and gas field development optimization: Current status and future directions

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Petroleum Science 2025年第1期22卷 508-526页

作者： Auref Rostamian Matheus Bernardelli de Moraes Denis José Schiozer Guilherme Palermo Coelho School of Mechanical Engineering Center for Energy and Petroleum Studies (CEPETRO) Universidade Estadual de Campinas School of Technology (FT) University of Campinas (UNICAMP)

In the area of reservoir engineering, the optimization of oil and gas production is a complex task involving a myriad of interconnected decision variables shaping the production system's ***, this optimization process was centered on a single objective, such as net present value,return on investment, cumulative oil production, or cumulative water production. However, the inherent complexity of reservoir exploration necessitates a departure from this single-objective approach. Multiple conflicting production and economic indicators must now be considered to enable more precise and robust decision-making. In response to this challenge, researchers have embarked on a journey to explore field development optimization of multiple conflicting criteria, employing the formidable tools of multi-objective optimization algorithms. These algorithms delve into the intricate terrain of production strategy design, seeking to strike a delicate balance between the often-contrasting objectives. Over the years, a plethora of these algorithms have emerged, ranging from a priori methods to a posteriori approach, each offering unique insights and capabilities. This survey endeavors to encapsulate, categorize, and scrutinize these invaluable contributions to field development optimization, which grapple with the complexities of multiple conflicting objective functions. Beyond the overview of existing methodologies, we delve into the persisting challenges faced by researchers and practitioners ***, the application of multi-objective optimization techniques to production optimization is hindered by the resource-intensive nature of reservoir simulation, especially when confronted with inherent uncertainties. As a result of this survey, emerging opportunities have been identified that will serve as catalysts for pivotal research endeavors in the future. As intelligent and more efficient algorithms continue to evolve, the potential for addressing hitherto ins

关键词： Derivative-free algorithms Ensemble-based optimization gradient-based methods Life-cycle optimization Reservoir field development and management

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Learning of Fuzzy Cognitive Map models without training data

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NEUROCOMPUTING 2025年 623卷

作者： Napoles, Gonzalo Grau, Isel Concepcion, Leonardo Salgueiro, Yamisleydi Vanhoof, Koen Tilburg Univ Dept Cognit Sci & Artificial Intelligence Tilburg Netherlands UHasselt Business Informat Res Grp Hasselt Belgium Eindhoven Univ Technol Dept Ind Engn & Innovat Sci Eindhoven Netherlands Eindhoven Univ Technol Eindhoven Artificial Intelligence Syst Inst Eindhoven Netherlands Univ Cent Las Villas Santa Clara Cuba Univ Talca Fac Engn Dept Ind Technol Campus Curico Curico Chile

This paper introduces a novel zero-data learning algorithm tailored for Fuzzy Cognitive Map (FCM) models utilized in control applications where we must maintain concepts' activation values within predefined intervals. Our approach allows domain experts to specify these intervals and optionally impose weight constraints, ensuring the algorithm produces feasible models. At the core of our approach lies a mathematical formalism that approximates the smallest feasible activation space for each neural concept, which translates into lower and upper bounds for concepts' activation values. Moreover, a parameterized quasi-nonlinear reasoning rule allows controlling whether or not the network converges to a unique fixed point. The learning goal of our algorithm narrows down to computing a weight matrix minimizing the error between the analytical bounds and the target intervals specified by domain experts. To address such a constrained minimization problem, we employ numerical methods operating with approximate gradients, which provide highly accurate solutions with short execution times. The main contribution of our learning algorithm is that it does not require any training data to compute the network structure. Therefore, by accurately approximating the specified activation intervals, our learning algorithm guarantees that the outputs produced by the FCM model will remain within these intervals regardless of the initial conditions used to start the recurrent reasoning process.

关键词： Fuzzy cognitive maps gradient-based methods Simulation and control Zero-data learning

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Accelerated first-order optimization under nonlinear constraints

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MATHEMATICAL PROGRAMMING 2025年 1-46页

作者： Muehlebach, Michael Jordan, Michael I. Max Planck Inst Intelligent Syst Learning & Dynam Syst Max Planck Ring 4 D-72076 Tubingen Baden Wuerttemb Germany Univ Calif Berkeley Dept Elect Engn & Comp Sci 387 Soda Hall Berkeley CA 94720 USA

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected gradients, these algorithms avoid optimization over the entire feasible set at each iteration. We prove convergence to stationary points even in a nonconvex setting and we derive accelerated rates for the convex setting both in continuous time, as well as in discrete time. An important property of these algorithms is that constraints are expressed in terms of velocities instead of positions, which naturally leads to sparse, local and convex approximations of the feasible set (even if the feasible set is nonconvex). Thus, the complexity tends to grow mildly in the number of decision variables and in the number of constraints, which makes the algorithms suitable for machine learning applications. We apply our algorithms to a compressed sensing and a sparse regression problem, showing that we can treat nonconvex & ell;(p) constraints (p<1) efficiently, while recovering state-of-the-art performance for p=1.

关键词： Constrained optimization Nonlinear programming gradient-based methods Machine learning

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A Comparative Study of gradient-Type methods for Recovering Time-Dependent Heat Sources

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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2013年第9期38卷 2545-2556页

作者： Rezapour, Javad Molavi, Hosein Daneshian, Behrouz Bahrami, Hamid Reza Talesh Islamic Azad Univ Dept Mech Engn Lahijan Branch Lahijan 1616 Iran Islamic Azad Univ Lahijan Branch Dept Math Lahijan 1616 Iran

gradient-based methods belong to offline techniques which use all the available data reading to set the unknown thermal coefficients. General application and rigorous mathematical investigation of these methods make them robust tools for analyzing inverse heat problems. In the present study, four search techniques in gradient-type methods through the use of adjoint problem are employed for the evaluation of heat sources in arbitrary geometries. The methods include Fletcher-Reeves version of the conjugate gradient method (CGM), Hestenes-Stiefel version of the CGM, Broydon-Fletcher-Goldfarb-Shanno version of quasi-Newton method and a novel form of the gradient-type method. The search direction in the novel method appears to have originated as a hybridization of a conjugate gradient and a quasi-Newton method. A conservative cell-based version of finite volume scheme is applied for the solution of heat-conduction problem in irregular domains. To highlight the flexibility and advantages of these algorithms, their performance and accuracy are presented and compared for two-dimensional heat-conduction problems.

关键词： gradient-based methods Heat sources Inverse heat conduction

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Multi-frame estimation of planar motion

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2000年第10期22卷 1105-1116页

作者： Zelnik-Manor, L Irani, M Weizmann Inst Sci Dept Comp Sci & Appl Math IL-76100 Rehovot Israel

Traditional plane alignment techniques are typically performed between pairs of frames. In this paper, we present a method for extending existing two-frame planar motion estimation techniques into a simultaneous multi-frame estimation, by exploiting multiframe subspace constraints of planar surfaces. The paper has three main contributions: 1) we show that when the camera calibration does not change, the collection of all parametric image motions of a planar surface in the scene across multiple frames is embedded in a low dimensional linear subspace;2) we show that the relative image motion of multiple planar surfaces across multiple frames is embedded in a yet lower dimensional linear subspace, even with varying camera calibration;and 3) we show how these multi-frame constraints can be incorporated into simultaneous multi-frame estimation of planar motion, without explicitly recovering any 3D information, or camera calibration. The resulting multi-frame estimation process is more constrained than the individual two-frame estimations, leading to more accurate alignment, even when applied to small image regions.

关键词： motion estimation plane alignment multi-frame analysis gradient-based methods

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A unified square-root approach for the score and Fisher information matrix computation in linear dynamic systems

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MATHEMATICS AND COMPUTERS IN SIMULATION 2016年 119卷 128-141页

作者： Kulikova, M. V. Tsyganova, J. V. Univ Lisbon Inst Super Tecn CEMAT P-1049001 Lisbon Portugal Ulyanovsk State Univ Ulyanovsk 432017 Russia

One of the most frequently encountered problems in practice is to combine a priori knowledge about a physical system with experimental data to provide on-line estimation of an unknown dynamic state and system parameters. The classical way for solving this problem is to use adaptive filtering techniques. The adaptive schemes for the maximum likelihood estimation based on gradient-based optimization methods are, in general, preferable. They require the likelihood function and its gradient evaluation (score), and might demand the Fisher information matrix (FIM) computation. All techniques for the score and the FIM calculation in linear dynamic systems yield the implementation of the Kalman filter (KF) and its derivatives (with respect to unknown system parameters), which is known to be numerically unstable. An alternative solution can be found among algorithms developed in the KF community for solving ill conditioned problems: the square-root algorithms, the UD-based factorization methods and the fast SR Chandrasekhar-Kailath-Morf-Sidhu techniques. Recently, these advanced KF implementations have been extended on the filter derivatives computation. However there is no systematic way of designing the robust "differentiated" methods. In this paper, we develop a unified square-root methodology of generating the computational techniques for the filter/smoother derivatives evaluation required in gradient-based adaptive schemes for the score and the FIM computation. (C) 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： Kalman filtering Maximum likelihood estimation gradient-based methods Fisher information matrix Square-root algorithms

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Optimal control of impulsive hybrid systems

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NONLINEAR ANALYSIS-HYBRID SYSTEMS 2008年第4期2卷 1089-1097页

作者： Azhmyakov, V. Boltyanski, V. G. Poznyak, A. CINVESTAV Dept Control Automat Mexico City 07360 DF Mexico CIMAT Guanajuato 36000 Mexico

In this paper, we deal with optimization techniques for a class of hybrid systems that comprise continuous controllable dynamics and impulses (jumps) in the state. Using the mathematical techniques of distributional derivatives and impulse differential equations, we rewrite the original hybrid control system as a system with autonomous location transitions. For the obtained auxiliary dynamical system and the corresponding optimal control problem (OCP), we apply the Lagrange approach and derive the reduced gradient formulas. Moreover, we formulate necessary optimality conditions for the above hybrid OCPs, and discuss the newly elaborated Pontryagin-type Maximum Principle for impulsive OCPs. As in the case of the conventional OCPs, the proposed first order optimization techniques provide a basis for constructive computational algorithms. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Hybrid control systems Optimal control gradient-based methods Necessary conditions of optimality

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